## skullpatrol Group Title Does 0.999...=1? one year ago one year ago

1. zzr0ck3r Group Title

.9999........ is not a number

2. zzr0ck3r Group Title

have you taken calculus?

3. zzr0ck3r Group Title
4. zzr0ck3r Group Title

scroll down to number 4, its actaully an easy proof.

5. zzr0ck3r Group Title

you will enjoy calculus:)

6. carson889 Group Title

Here is an algebraic proof of it: 10x = 9.999999... with x = 0.99999... 10x - x = 9.99999... - 0.999999... 9x = 9 Thus, x = 1

7. zzr0ck3r Group Title

This question was asked because I was trying to exaplin that inbetween any two numbers is another number, he then said what about .9999999.... and 1, i then tried to explain to him that .99999999.. was not a finite number, then we had this question posted:)

8. zzr0ck3r Group Title

there is no amount of 9's that you can write after .9 that will make it equal to 1, but the limit as the amount of 9's goes to infinity is said to equal 1

9. ByteMe Group Title

wait... doesn't 0.9999... = 9/10 + 9/100 + 9/1000 + .... an infinite bounded series?

10. mayankdevnani Group Title

The number "0.9999..." can be "expanded" as: 0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

11. mayankdevnani Group Title

12. mayankdevnani Group Title

13. zzr0ck3r Group Title

lol, read this. then you will see the point of the question http://openstudy.com/study#/updates/50ab1ceee4b06b5e49334d38

14. mayankdevnani Group Title

So the formula proves that 0.9999... = 1.

15. mayankdevnani Group Title

@skullpatrol ok

16. zzr0ck3r Group Title

but .99999...is not a number is the point of this topic

17. mayankdevnani Group Title

0.999999..... is a no. we have tp prove that it is equal to 1

18. mayankdevnani Group Title

*to

19. zzr0ck3r Group Title

its a number if you think about convergence, but you can never write 1 in the form .999999999999, read the last question and you will see the point im trying to make

20. zzr0ck3r Group Title

its not a finite number.... it can be looked at as a sequence....at infinity then its a number. I told him that between any two numbers is another number, he then said what about .99999999999..... and 1, this is what followed.

21. zzr0ck3r Group Title

Its an extended real number in the since that infinity is an extended real number....

22. mayankdevnani Group Title

"But", some say, "there will always be a difference between 0.9999... and 1." Well, sort of. Yes, at any given stop, at any given stage of the expansion, for any given finite number of 9s, there will be a difference between 0.999...9 and 1. That is, if you do the subtraction, 1 – 0.999...9 will not equal zero. But the point of the "dot, dot, dot" is that there is no end; 0.9999... is inifinte. There is no "last" digit. So the "there's always a difference" argument betrays a lack of understanding of the infinite. (That's not a "criticism", per se; infinity is a messy topic.)

23. zzr0ck3r Group Title

right and i dont think he has had calculus...

24. zzr0ck3r Group Title

this started with density of rational/irational and archimedes principle on the real line

25. zzr0ck3r Group Title

the point is, that there is an infinite amount of numbers between any two numbers a,b where a != b

26. mayankdevnani Group Title

hahhaha.. we are just fighting you and me are absolutely right...it's a skull problem..right??

27. mayankdevnani Group Title

right?? @zzr0ck3r

28. zzr0ck3r Group Title

This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)

29. zzr0ck3r Group Title

right:)

30. mayankdevnani Group Title

:)

31. waterineyes Group Title

0.9999 is approximately equal to 1 but it is not exactly equal.. $0.999 \approx 1 \qquad \qquad (0.999 \ne 1)$

32. mayankdevnani Group Title

got it @skullpatrol

33. mayankdevnani Group Title

this question...lol

34. mayankdevnani Group Title
35. Zarkon Group Title

can you provide a proof of this ... "This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)"

36. zzr0ck3r Group Title

no, my analysis teacher said it two days ago. she said the elemnts between 0 and 1 have more mappings than 0-infinity

37. Zarkon Group Title

your teacher is either wrong or you have misquoted her

38. Zarkon Group Title

the real numbers between 0 and 1 is the same size as the real numbers from 0 to infinity

39. ParthKohli Group Title

$1 - 0.999\cdots = 0.000\cdots = 0$